So obviously blunt weapons are your best choice for taking down undead, since they're immune to organ damage and can't feel pain. Your only real hope is to smash in their face, particularly in the case of zombies. Skeletons you can take down with a sword, since just a little damage and their arms'll fly off... however, if you're stuck with a spear and you're fighting a zombie, I've found your best bet is to drop the spear, grab the zombie with your shield and punch it until it dies. It actually works pretty well, even against elite weapon-users -- since they're so slow, you can get in and grab them by the weapon and then begin punching through their chests.
Anyone else know of effective methods for dispatching the undead?